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The Fixed Job Schedule Problem with Working-Time Constraints

Author

Listed:
  • Matteo Fischetti

    (University of Bologna, Bologna, Italy)

  • Silvano Martello

    (University of Bologna, Bologna, Italy)

  • Paolo Toth

    (University of Bologna, Bologna, Italy)

Abstract

We consider a generalization of the fixed job schedule problem where a bound is imposed on the total working time of each processor. It is shown that the problem is NP-hard but polynomially solvable in the preemptive case. We introduce several lower bounds. One is determined through definition of a special class of graphs, for which the maximum clique problem is shown to be polynomial. Lower bounds and dominance criteria are exploited in a branch-and-bound algorithm for optimal solution of the problem. The effectiveness of the algorithm is analyzed through computational experiments.

Suggested Citation

  • Matteo Fischetti & Silvano Martello & Paolo Toth, 1989. "The Fixed Job Schedule Problem with Working-Time Constraints," Operations Research, INFORMS, vol. 37(3), pages 395-403, June.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:3:p:395-403
    DOI: 10.1287/opre.37.3.395
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    Citations

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    Cited by:

    1. Markó Horváth & Tamás Kis, 2019. "Computing strong lower and upper bounds for the integrated multiple-depot vehicle and crew scheduling problem with branch-and-price," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 39-67, March.
    2. Krishnamoorthy, M. & Ernst, A.T. & Baatar, D., 2012. "Algorithms for large scale Shift Minimisation Personnel Task Scheduling Problems," European Journal of Operational Research, Elsevier, vol. 219(1), pages 34-48.
    3. Türsel Eliiyi, Deniz & Azizoglu, Meral, 2011. "Heuristics for operational fixed job scheduling problems with working and spread time constraints," International Journal of Production Economics, Elsevier, vol. 132(1), pages 107-121, July.
    4. Bastian Amberg & Boris Amberg & Natalia Kliewer, 2019. "Robust Efficiency in Urban Public Transportation: Minimizing Delay Propagation in Cost-Efficient Bus and Driver Schedules," Service Science, INFORMS, vol. 53(1), pages 89-112, February.
    5. Fang, Kan & Wang, Shijin & Pinedo, Michael L. & Chen, Lin & Chu, Feng, 2021. "A combinatorial Benders decomposition algorithm for parallel machine scheduling with working-time restrictions," European Journal of Operational Research, Elsevier, vol. 291(1), pages 128-146.
    6. Ingmar Steinzen & Vitali Gintner & Leena Suhl & Natalia Kliewer, 2010. "A Time-Space Network Approach for the Integrated Vehicle- and Crew-Scheduling Problem with Multiple Depots," Transportation Science, INFORMS, vol. 44(3), pages 367-382, August.
    7. Kroon, Leo G. & Salomon, Marc & Van Wassenhove, Luk N., 1995. "Exact and approximation algorithms for the operational fixed interval scheduling problem," European Journal of Operational Research, Elsevier, vol. 82(1), pages 190-205, April.
    8. Dennis Huisman & Richard Freling & Albert P. M. Wagelmans, 2005. "Multiple-Depot Integrated Vehicle and Crew Scheduling," Transportation Science, INFORMS, vol. 39(4), pages 491-502, November.
    9. Arpan Rijal & Marco Bijvank & Asvin Goel & René de Koster, 2021. "Workforce Scheduling with Order-Picking Assignments in Distribution Facilities," Transportation Science, INFORMS, vol. 55(3), pages 725-746, May.
    10. Matteo Fischetti & Andrea Lodi & Silvano Martello & Paolo Toth, 2001. "A Polyhedral Approach to Simplified Crew Scheduling and Vehicle Scheduling Problems," Management Science, INFORMS, vol. 47(6), pages 833-850, June.
    11. Kroon, Leo G. & Edwin Romeijn, H. & Zwaneveld, Peter J., 1997. "Routing trains through railway stations: complexity issues," European Journal of Operational Research, Elsevier, vol. 98(3), pages 485-498, May.
    12. Bekki, Özgün BarIs & Azizoglu, Meral, 2008. "Operational fixed interval scheduling problem on uniform parallel machines," International Journal of Production Economics, Elsevier, vol. 112(2), pages 756-768, April.
    13. A. Mingozzi & M. A. Boschetti & S. Ricciardelli & L. Bianco, 1999. "A Set Partitioning Approach to the Crew Scheduling Problem," Operations Research, INFORMS, vol. 47(6), pages 873-888, December.
    14. Antoon W.J. Kolen & Jan Karel Lenstra & Christos H. Papadimitriou & Frits C.R. Spieksma, 2007. "Interval scheduling: A survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 530-543, August.
    15. Knut Haase & Guy Desaulniers & Jacques Desrosiers, 2001. "Simultaneous Vehicle and Crew Scheduling in Urban Mass Transit Systems," Transportation Science, INFORMS, vol. 35(3), pages 286-303, August.
    16. Pan, Hanchuan & Liu, Zhigang & Yang, Lixing & Liang, Zhe & Wu, Qiang & Li, Sijie, 2021. "A column generation-based approach for integrated vehicle and crew scheduling on a single metro line with the fully automatic operation system by partial supervision," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).

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